A report on an ergodic dichotomy
Resumen:
We establish (some directions of) a Ledrappier correspondence between Hölder cocycles, Patterson–Sullivan measures, etc for word-hyperbolic groups with metric-Anosov Mineyev flow. We then study Patterson–Sullivan measures for ϑ-Anosov representations over a local field and show that these are parameterized by the ϑ-critical hypersurface of the representation. We use these Patterson–Sullivan measures to establish a dichotomy concerning directions in the interior of the ϑ-limit cone of the representation in question: if u is such a half-line, then the subset of u-conical limit points has either total mass if |ϑ| ≤ 2 or zero mass if |ϑ| ≥ 4. The case |ϑ| = 3 remains unsettled.
| 2024 | |
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ANOSOV REPRESENTATIONS PATTERSON–SULLIVAN MEASURES SKEW-PRODUCTS OVER SUBSHIFTS |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/44989 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
| _version_ | 1807522930834276352 |
|---|---|
| author | Sambarino, Andrés |
| author_facet | Sambarino, Andrés |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Sambarino Andrés, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| dc.creator.none.fl_str_mv | Sambarino, Andrés |
| dc.date.accessioned.none.fl_str_mv | 2024-07-30T14:58:06Z |
| dc.date.available.none.fl_str_mv | 2024-07-30T14:58:06Z |
| dc.date.issued.none.fl_str_mv | 2024 |
| dc.description.abstract.none.fl_txt_mv | We establish (some directions of) a Ledrappier correspondence between Hölder cocycles, Patterson–Sullivan measures, etc for word-hyperbolic groups with metric-Anosov Mineyev flow. We then study Patterson–Sullivan measures for ϑ-Anosov representations over a local field and show that these are parameterized by the ϑ-critical hypersurface of the representation. We use these Patterson–Sullivan measures to establish a dichotomy concerning directions in the interior of the ϑ-limit cone of the representation in question: if u is such a half-line, then the subset of u-conical limit points has either total mass if |ϑ| ≤ 2 or zero mass if |ϑ| ≥ 4. The case |ϑ| = 3 remains unsettled. |
| dc.format.extent.es.fl_str_mv | 54 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Sambarino , A. "A report on an ergodic dichotomy" Ergodic Theory and Dynamical Systems. [en linea] 2024; 44(1):236-289. 54 h. DOI: 10.1017/etds.2023.13. |
| dc.identifier.doi.none.fl_str_mv | 10.1017/etds.2023.13 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/44989 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | Cambridge University Press |
| dc.relation.ispartof.es.fl_str_mv | Ergodic Theory and Dynamical Systems. 2024; 44(1):236-289. doi:10.1017/etds.2023.13 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución (CC - By 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.other.es.fl_str_mv | ANOSOV REPRESENTATIONS PATTERSON–SULLIVAN MEASURES SKEW-PRODUCTS OVER SUBSHIFTS |
| dc.title.none.fl_str_mv | A report on an ergodic dichotomy |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | We establish (some directions of) a Ledrappier correspondence between Hölder cocycles, Patterson–Sullivan measures, etc for word-hyperbolic groups with metric-Anosov Mineyev flow. We then study Patterson–Sullivan measures for ϑ-Anosov representations over a local field and show that these are parameterized by the ϑ-critical hypersurface of the representation. We use these Patterson–Sullivan measures to establish a dichotomy concerning directions in the interior of the ϑ-limit cone of the representation in question: if u is such a half-line, then the subset of u-conical limit points has either total mass if |ϑ| ≤ 2 or zero mass if |ϑ| ≥ 4. The case |ϑ| = 3 remains unsettled. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_927d2bde0b43a2ec059e3b773ab3355e |
| identifier_str_mv | Sambarino , A. "A report on an ergodic dichotomy" Ergodic Theory and Dynamical Systems. [en linea] 2024; 44(1):236-289. 54 h. DOI: 10.1017/etds.2023.13. 10.1017/etds.2023.13 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/44989 |
| publishDate | 2024 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución (CC - By 4.0) |
| spelling | Sambarino Andrés, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2024-07-30T14:58:06Z2024-07-30T14:58:06Z2024Sambarino , A. "A report on an ergodic dichotomy" Ergodic Theory and Dynamical Systems. [en linea] 2024; 44(1):236-289. 54 h. DOI: 10.1017/etds.2023.13.https://hdl.handle.net/20.500.12008/4498910.1017/etds.2023.13We establish (some directions of) a Ledrappier correspondence between Hölder cocycles, Patterson–Sullivan measures, etc for word-hyperbolic groups with metric-Anosov Mineyev flow. We then study Patterson–Sullivan measures for ϑ-Anosov representations over a local field and show that these are parameterized by the ϑ-critical hypersurface of the representation. We use these Patterson–Sullivan measures to establish a dichotomy concerning directions in the interior of the ϑ-limit cone of the representation in question: if u is such a half-line, then the subset of u-conical limit points has either total mass if |ϑ| ≤ 2 or zero mass if |ϑ| ≥ 4. The case |ϑ| = 3 remains unsettled.Submitted by Egaña Florencia (florega@gmail.com) on 2024-07-29T15:59:49Z No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.101etds2023.13.pdf: 461974 bytes, checksum: defad4e00a30c05bbb10589755a2bab0 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-07-30T14:43:49Z (GMT) No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.101etds2023.13.pdf: 461974 bytes, checksum: defad4e00a30c05bbb10589755a2bab0 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-07-30T14:58:06Z (GMT). No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.101etds2023.13.pdf: 461974 bytes, checksum: defad4e00a30c05bbb10589755a2bab0 (MD5) Previous issue date: 202454 h.application/pdfenengCambridge University PressErgodic Theory and Dynamical Systems. 2024; 44(1):236-289. doi:10.1017/etds.2023.13Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC - By 4.0)ANOSOV REPRESENTATIONSPATTERSON–SULLIVAN MEASURESSKEW-PRODUCTS OVERSUBSHIFTSA report on an ergodic dichotomyArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaSambarino, AndrésLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/44989/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/44989/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-820496http://localhost:8080/xmlui/bitstream/20.500.12008/44989/3/license_texta34a400dd0046b3aef60f72471c4f991MD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | A report on an ergodic dichotomy Sambarino, Andrés ANOSOV REPRESENTATIONS PATTERSON–SULLIVAN MEASURES SKEW-PRODUCTS OVER SUBSHIFTS |
| status_str | publishedVersion |
| title | A report on an ergodic dichotomy |
| title_full | A report on an ergodic dichotomy |
| title_fullStr | A report on an ergodic dichotomy |
| title_full_unstemmed | A report on an ergodic dichotomy |
| title_short | A report on an ergodic dichotomy |
| title_sort | A report on an ergodic dichotomy |
| topic | ANOSOV REPRESENTATIONS PATTERSON–SULLIVAN MEASURES SKEW-PRODUCTS OVER SUBSHIFTS |
| url | https://hdl.handle.net/20.500.12008/44989 |
